1. Field of the Invention
The present invention relates to an apparatus, a method, a storage medium, and a computer program product for performing proximity effect correction in exposing a mask pattern by lithography.
2. Description of the Related Art
A demand for a finer semiconductor circuit has been recently increasing and an influence of a proximity effect as a result of making the circuit finer is becoming a matter which is not negligible. This influence of the proximity effect has brought about a problem that a semiconductor circuit as designed cannot be manufactured. Accordingly, processing called proximity effect correction is performed in which the influence of the proximity effect is previously understood and design data is changed in advance so that a desired size can be obtained.
Conventional proximity effect correction processing has been performed by, in a side of an object to be corrected, calculating the distance to adjacent sides calculated in a perpendicular direction, a size of the object to which the side belongs, the distance to a side further beyond the object, and the like, and defining a proximity effect correction rule adaptable to these values.
However, the definition of the correction rule is limited and a complicated form and the like are difficult to be represented by the rule. Therefore, the use of a simulator has been recently considered as a means for obtaining a sufficient correction effect even in a state in which a mask pattern is complicatedly arranged.
When proximity effect correction using the simulator is performed, it is general to first obtain and use the light intensity distribution for a certain fixed region including the object to be corrected. Incidentally, since the calculated light intensity distribution is discrete, light intensity values of necessary points are obtained by linear interpolation.
In obtaining the light intensity distribution, a Fourier-transform image of the mask pattern is first obtained and then processing called fast-Fourier-transform (FFT) is performed so as to obtain the light intensity distribution. The number of times T1 of processing arithmetic in performing one-dimensional FFT is represented by the following equation.T1=Nlog2(N)
Here, N is the lattice number of the points for which the light intensity distribution is obtained. For example, when N=8, T1=24. The lattice number in actually obtaining the light intensity distribution is N=300 considering a range of 3 μm in increments of 0.01 μm. Here, N needs to be a power of 2 when FFT is used, the numbers such as N=256, 512, and the like are used.
On the other hand, the number of times T2 of processing arithmetic in performing two-dimensional FFT is represented by the following equation.T2=N3log2(N)
Here, the number of calculation times 2 needed in obtaining the light intensity distribution of the lattice number of 256×256 is 1.3×108.
As described above, an optimal form for proximity effect correction can be derived by simulating an exposure result at every necessary time if the simulator is used but, on the other hand, there is a problem that correction processing takes long time and it is unrealistic in terms of processing time to obtain the light intensity distribution for all the regions of an enormous amount of design data.
Further, any method for performing appropriate proximity effect correction is not provided currently for a case in which the object to be corrected does not have the desired form.